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Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime's square). In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit.
The sieve methods discussed in this article are not closely related to the integer factorization sieve methods such as the quadratic sieve and the general number field sieve. Those factorization methods use the idea of the sieve of Eratosthenes to determine efficiently which members of a list of numbers can be completely factored into small primes.
Eratosthenes created a whole section devoted to the examination of Homer, and acquired original works of great tragic dramas of Aeschylus, Sophocles and Euripides. [6] Eratosthenes made several important contributions to mathematics and science, and was a friend of Archimedes. Around 255 BC, he invented the armillary sphere.
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
Sieve method, or the method of sieves, can mean: in mathematics and computer science, the sieve of Eratosthenes, a simple method for finding prime numbers in number theory, any of a variety of methods studied in sieve theory; in combinatorics, the set of methods dealt with in sieve theory or more specifically, the inclusion–exclusion principle
In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory.It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds on the number of primes within a given set of integers.
The Byte Sieve is a computer-based implementation of the Sieve of Eratosthenes published by Byte as a programming language performance benchmark.It first appeared in the September 1981 edition of the magazine and was revisited on occasion.
In mathematics, the sieve of Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up to a specified integer. It was discovered by Indian student S. P. Sundaram in 1934.